Determining the effects of lake variables on the relationship of TP (log transformed ug/L) with Chl-a concentrations (log transformed ug/L), using the gradient of residuals against variables.

Linear model of logCHLA~logTP

Initial log-transformed linear model

Scatterplot

lm1 <- lm(logCHLA~logTP, data=df)
df$res.lm <- resid(lm1)

plot.lm1 <- ggplot(df,aes(x=logTP,y=logCHLA))+
  geom_point()+
  geom_smooth(method='lm')+
  labs(title="Linear log-log model",x="log TP",y="log CHLA")
print(plot.lm1)

## `geom_smooth()` using formula 'y ~ x'

Model statistics

summary(lm1)

## 
## Call:
## lm(formula = logCHLA ~ logTP, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.6584 -0.4638  0.0539  0.5754  4.5151 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.91854    0.06877   86.06   <2e-16 ***
## logTP        1.03301    0.01594   64.80   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.942 on 6467 degrees of freedom
## Multiple R-squared:  0.3937, Adjusted R-squared:  0.3936 
## F-statistic:  4199 on 1 and 6467 DF,  p-value: < 2.2e-16

anova(lm1)

## Analysis of Variance Table
## 
## Response: logCHLA
##             Df Sum Sq Mean Sq F value    Pr(>F)    
## logTP        1 3726.0  3726.0  4198.9 < 2.2e-16 ***
## Residuals 6467 5738.7     0.9                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual plots

Remove outliers and rerun model

Identify outliers

Outliers were identified as points with studentized residuals outside 3:-3

Scatterplot without outliers

plot.lm2<- ggplot(df2,aes(x=logTP,y=logCHLA))+
  geom_point()+
  geom_smooth(method='lm')+
  labs(title="Linear log-log model without outliers",x="log TP",y="log CHLA")
print(plot.lm2)

## `geom_smooth()` using formula 'y ~ x'

Model statistics

summary(lm2)

## 
## Call:
## lm(formula = logCHLA ~ logTP, data = df2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.98289 -0.46847  0.03455  0.53092  2.81817 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.30320    0.06207  101.55   <2e-16 ***
## logTP        1.11344    0.01439   77.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8251 on 6362 degrees of freedom
## Multiple R-squared:  0.4849, Adjusted R-squared:  0.4848 
## F-statistic:  5988 on 1 and 6362 DF,  p-value: < 2.2e-16

anova(lm2)

## Analysis of Variance Table
## 
## Response: logCHLA
##             Df Sum Sq Mean Sq F value    Pr(>F)    
## logTP        1 4076.5  4076.5  5988.1 < 2.2e-16 ***
## Residuals 6362 4331.0     0.7                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual plots

Variable effects on model residuals

Relationship of model residuals to lake characteristic variables

Residual plots

Pattern of logCHLA~logTP model residuals along gradients of variables. All variables are fitted to a linear model on the residuals.

cols <- c(2,9,10,11,15,16)

df2 <- df2 %>%
  rename("Sample date"=SAMPLE_DATE,
         "Secchi disk depth"=`DEPTH, SECCHI DISK DEPTH_SD_NA`,
         "Log(N:P)"=NPratio,
         "Lake temperature"=`TEMPERATURE, WATER_OW_NA`,
         "True color"=`TRUE COLOR_OW_T`)

for(i in cols){
  lm.loop <- lm(res.lm ~ df2[,i], data=df2) #linear model of residuals against variable
  p1 <- ggplot(df2,aes(x=df2[,i],y=res.lm))+
    geom_point()+
    geom_smooth(method='lm')+ 
    labs(x=paste(colnames(df2[i])),
         y='residuals of LM(logCHLA~logTP)')
  if(colnames(df2[i])=="Sample date"){
    p1 <- p1+scale_x_date(date_labels="%Y")
  }
  p2 <- ggplot(data=df2, aes(x=df2[,i])) +
    geom_density(fill="grey") +
    theme(axis.title.x=element_blank(),
        axis.text.x=element_blank(),
        axis.ticks.x=element_blank(),
        axis.title.y=element_blank(),
        axis.text.y=element_blank(),
        axis.ticks.y=element_blank(),
        panel.grid=element_blank(),
        axis.line=element_blank(),
        panel.background = element_blank())
  if(i==11){
    dat <- df2
    dat[,i]<-log(as.numeric(df2[,i]))
    dat <- dat %>%
      select(res.lm,"Log(N:P)") %>%
      na.omit(dat)
    dat <- dat[!is.infinite(dat$`Log(N:P)`),]
    lm.loop <- lm(res.lm ~ `Log(N:P)`,dat) 
    p1 <- ggplot(dat,aes(x=`Log(N:P)`,y=res.lm))+
      geom_point()+
      geom_smooth(method='lm')+ 
      labs(x=paste(colnames(df2[i])),
           y='residuals of LM(logCHLA~logTP)')
    p2 <- ggplot(data=dat, aes(x=`Log(N:P)`)) +
      geom_density(fill="grey") +
      theme(axis.title.x=element_blank(),
            axis.text.x=element_blank(),
            axis.ticks.x=element_blank(),
            axis.title.y=element_blank(),
            axis.text.y=element_blank(),
            axis.ticks.y=element_blank(),
            panel.grid=element_blank(),
            axis.line=element_blank(),
            panel.background = element_blank())
    }
  require(gridExtra)
  grid.arrange(p2, p1, ncol = 1, heights = c(1, 4))
  stats[nrow(stats)+1,] <- c(colnames(df2[i]),
                             coef(lm.loop),
                             summary(lm.loop)$coefficients[2,4],
                             summary(lm.loop)$r.squared)
  vars[nrow(vars)+1,] <- c(colnames(df2)[i],
                           paste(min(as.numeric(na.omit(df2[,i]))),
                                 "-",max(as.numeric(na.omit(df2[,i])))),
                           nrow(df2[i]),
                           paste(median(as.numeric(na.omit(df2[,i]))),
                           "(",summary(as.numeric(na.omit(df2[,i])))[2],
                           "-",summary(as.numeric(na.omit(df2[,i])))[5],")")) #stats
}

Model statistics

Variable descriptive statistics

characteristic	range	n	median..IQR.
Sample date	6007 - 18535	6364	12687 ( 8230.75 - 15877 )
Secchi disk depth	0.05 - 13.6	6364	3.3 ( 2 - 4.75 )
NITROGEN, NITRATE-NITRITE_OW_T	-0.000798 - 2.3	6364	0.01 ( 0.009922 - 0.034 )
Log(N:P)	-0.0973170731707317 - 283.333333333333	6364	1.01386281588448 ( 0.509259259259259 - 2.96805309734513 )
Lake temperature	4 - 36	6364	22.7777777777778 ( 20 - 25 )
True color	0 - 222	6364	10 ( 6 - 19 )
ACID DEPOSITION	213.6579857 - 1671.703552	2985	808.8840129 ( 465.2497559 - 975.3500061 )
PRECIPITATION	76.6439971923828 - 192.690994262695	2515	105.960250854492 ( 96.1419982910156 - 119.623184926382 )
COLOR (LOW)	Inf - -Inf	5018	NA ( NA - NA )
COLOR (HIGH)	Inf - -Inf	1449	NA ( NA - NA )

Coefficients for linear models of residuals along gradient of variables. Bold values indicate significant p-values (<0.05). Sorted by rsquared.

characteristic	intercept	slope	p.value	rsquared
Secchi disk depth	0.54363702693813	-0.153747955259471	4.7134371288255e-174	0.120415808390344
ACID DEPOSITION	-0.631478072707592	0.000830913929983691	1.54946185732119e-68	0.0975389912152332
Sample date	0.781246097445401	-6.34720589943145e-05	5.71931741311346e-136	0.0922829965290701
Lake temperature	0.356610213342912	-0.0155339225932219	2.47318449824419e-07	0.00438824828642913
NITROGEN, NITRATE-NITRITE_OW_T	0.000554353651244087	-0.26192822098921	7.94789084060051e-05	0.00306853745689088
COLOR (LOW)	-0.0406983215745642	0.00612269831057828	0.00568369290808991	0.00155562297822806
PRECIPITATION	0.243824973482366	-0.00110609574794805	0.207023599057856	0.000633478591571892
Log(N:P)	-0.0138670292849897	-0.0132768640679941	0.0977693577900466	0.000541288958866251
COLOR (HIGH)	-0.23749465646799	0.0545782510659642	0.39803353719385	0.000531499162041898
True color	0.00554566259074965	-0.00029577409163138	0.672574876652699	2.85375728495901e-05

Most recent year

## Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...): NA/NaN/Inf in 'y'

## Error in `$<-.data.frame`(`*tmp*`, "DEPTH, BOTTOM_OW_NA", value = NA_real_): replacement has 1 row, data has 0

## Error in summary(lm.dep)$coefficients[2, 4]: subscript out of bounds

Recent year statistics

Variable descriptive statistics

characteristic	years	range	n	median..IQR.
Secchi disk depth	2018 - 2020	0.65 - 11.85	275	3.9 ( 2.25 - 5.25 )
NITROGEN, NITRATE-NITRITE_OW_T	2018 - 2020	0.0035 - 0.677	275	0.0209 ( 0.01 - 0.0713 )
LAKE DEPTH	2020 - 2020	11 - 11	9
ACID DEPOSITION (DIN:TP>1.5)	2011 - 2018	213.6579857 - 772.1180725	82
ACID DEPOISITION (DIN:TP<1.5)	2017 - 2018	213.6579857 - 712.899106	176
PRECIPITATION	2013 - 2016	76.9628023420061 - 131.316277313232	126
NITRATE+NITRITE (DIN:TP<1.5)	2017 - 2020	0.0035 - 0.118	140
NITRATE+NITRITE (DIN:TP>1.5)	2011 - 2020	0.01 - 0.677	72

Coefficients for linear models of residuals along gradient of variables in most recent year. Bold values indicate significant p-values (<0.05). Sorted by rsquared.

characteristic	intercept	slope	p.value	rsquared
Secchi disk depth	0.418879370452514	-0.134729328574692	2.07201547289412e-10	0.140652301284837
NITROGEN, NITRATE-NITRITE_OW_T	-0.0137309001466414	-1.25302057761975	0.0317085975993846	0.0525344583539137
NITRATE+NITRITE (DIN:TP>1.5)	-0.179923076337358	-0.932026609361253	0.123171988725382	0.0345933919602646
PRECIPITATION	0.548127466881036	-0.00939716704713627	0.229478947427043	0.0120115407499817
ACID DEPOSITION (DIN:TP>1.5)	-0.767947443943008	0.000989169049434624	0.389269420193164	0.00976922152200085
ACID DEPOSITION (DIN:TP<1.5)	-0.767947443943008	0.000989169049434624	0.389269420193164	0.00976922152200085
NITRATE+NITRITE (DIN:TP<1.5)	-0.0793890427344458	0.388563331374409	0.915696788224396	8.26930177312915e-05

Color bins

High vs low color, sample date [1] “HIGH COLOR, N= 0” [1] “LOW COLOR, N= 0”

## Error in eval(predvars, data, env): object 'SAMPLE_DATE' not found

## Error in FUN(X[[i]], ...): object 'SAMPLE_DATE' not found

## Error in coef(lm.high): object 'lm.high' not found

## Error in eval(predvars, data, env): object 'SAMPLE_DATE' not found

## Error in FUN(X[[i]], ...): object 'SAMPLE_DATE' not found

## Error in coef(lm.low): object 'lm.low' not found

characteristic	intercept	slope	p.value	rsquared

Color trend, sample date

## Error: Can't subset columns that don't exist.
## x Column `TRUE COLOR_OW_T` doesn't exist.

## Error: Can't subset columns that don't exist.
## x Column `TRUE COLOR_OW_T` doesn't exist.

[1] “INCREASING COLOR, N= 22” [1] “DECREASING COLOR, N= 17”

## Error in eval(predvars, data, env): object 'res.lm' not found

## Error in ggplot(lm.inc, aes(x = SAMPLE_DATE, y = res.lm)): object 'lm.inc' not found

## Error in ggplot(data = lm.inc, aes(x = SAMPLE_DATE)): object 'lm.inc' not found

## Error in FUN(X[[i]], ...): object 'SAMPLE_DATE' not found

## Error in coef(lm.inc): object 'lm.inc' not found

## Error in eval(predvars, data, env): object 'res.lm' not found

## Error in FUN(X[[i]], ...): object 'SAMPLE_DATE' not found

## Error in coef(lm.dec): object 'lm.dec' not found

characteristic	intercept	slope	p.value	rsquared

Relationship of model residuals to year by lake

Pattern of logCHLA~logTP model residuals along sample date for each lake. Data from each lake are fitted to a linear model on the residuals.

Residual plots

A red regression line indicates the model is statistically insignificant (p>0.05). A red border medians that the lake had a negative chlorophyll trend and a flat or positive phosphorous trend.

#each lake
#loop over each lake
LAKE_IDS <- unique(df$LAKE_ID) #list lakes
coeffs <- data.frame(lake=character(),
                     intercept=double(),
                     slope=double(),
                     'p-value'=double(),
                     rsquared=double()) #blank coefficient table

incongruous <- read.csv("~/OneDrive - New York State Office of Information Technology Services/Rscripts/Trend/chl-tp-lakes.csv")
incongruous <- incongruous[which(incongruous$CHL_slope!=incongruous$PHOS_slope),]
incongruous <- incongruous[incongruous$CHL_slope=="neg",]

for (i in 1:length(LAKE_IDS)) {
  lake <- LAKE_IDS[[i]] #pick a lake
  dat <- df2[df2$LAKE_ID == lake,] #create new data with that lake
  resid.loop <- lm(logCHLA~logTP,data=dat) #linear model of chl vs tp
  dat$res.loop <- resid(resid.loop) #residuals for that lake
  lm.loop <- lm(res.loop~SAMPLE_DATE,data=dat) #linear model of residuals vs year
  co <- coef(lm.loop)
  plot <- ggplot(dat,aes(x=SAMPLE_DATE,y=res.loop))+ #plot lake
    geom_point() +
    labs(title=paste(lake),x='year',y='residuals of LM(logCHLA~logTP)')
  if(summary(lm.loop)$coefficients[,4]<0.05){ #plot significant lakes
    plot <- plot + geom_smooth(method='lm')
  }else{
    plot <- plot + geom_smooth(method='lm',aes(color="red"),show.legend=FALSE)
  }
  if(lake %in% incongruous$LAKE_ID){
    plot <- plot + theme(panel.border = element_rect(colour = "red", fill=NA, size=3))
  }else{}
  print(plot) #print
  coeffs[nrow(coeffs)+1,] <- c(lake,
                               co,
                               summary(lm.loop)$coefficients[2,4],
                               summary(lm.loop)$r.squared)
}

## Error in eval(predvars, data, env): object 'SAMPLE_DATE' not found

Model statistics

Coefficients for linear models of residuals along gradient of time for each lake. Bold values indicate significant p-values (<0.05). Asterisks (***) indicate that the lake had a negative chlorophyll trend and a flat or positive phosphorous trend.

lake	intercept	slope	p.value	rsquared

Distribution of slopes

Dot plot of slope for each lake. Grey dots are statistically insignificant (p>0.05).

## Error in `$<-.data.frame`(`*tmp*`, x, value = "lakes"): replacement has 1 row, data has 0

## Error in `$<-.data.frame`(`*tmp*`, sig, value = "sig"): replacement has 1 row, data has 0

## Error in if (coeffs$p.value[i] < 0.05) {: missing value where TRUE/FALSE needed

## Error in FUN(X[[i]], ...): object 'x' not found

# Maps

temp1 <- read.csv("junk.sabrina.slopes2.csv") 

temp1 <- temp1 %>% 
  select(-c("ChlA","P","risiduals"))
coeffs2 <- coeffs %>%
  rename(LAKE_ID=lake) %>%
  rename(CHLTP=slope) %>%
  select(LAKE_ID,CHLTP,p.value)
coeffs2$CHLTP <- as.numeric(coeffs2$CHLTP)
coeffs2$p.value <- as.numeric(coeffs2$p.value)

coeffs2$CHLTP[coeffs2$p.value>0.05]<-0

slopes <- merge(temp1,coeffs2,by="LAKE_ID",all.x=TRUE,all.y=TRUE)

locs <- read.csv("/Users/sabrinaxie/New York State Office of Information Technology Services/BWAM - Lakes Database/Current/new_database/L_LOCATION.csv")

locs <- locs %>%
  filter(LOCATION_TYPE=="CENTROID") %>%
  select(LAKE_HISTORY_ID,LOCATION_X_COORDINATE,LOCATION_Y_COORDINATE) %>%
  rename(LAKE_ID=LAKE_HISTORY_ID)

sites<-merge(slopes,locs,by=c('LAKE_ID'),all.x = TRUE) %>%
  distinct()

library(ggmap)

## Google's Terms of Service: https://cloud.google.com/maps-platform/terms/.

## Please cite ggmap if you use it! See citation("ggmap") for details.

ggplot(grid, aes(lon, lat)) +
  geom_raster(aes(fill = cut(z, zCuts)))

## Error:   You're passing a function as global data.
##   Have you misspelled the `data` argument in `ggplot()`

#color
nybox<-make_bbox(sites,lon=LOCATION_X_COORDINATE,lat=LOCATION_Y_COORDINATE)
ny.map <- qmap(nybox,source="osm",color="bw")

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ny.map1<- ny.map +
  geom_point(data=sites,size=4,
             aes(x=LOCATION_X_COORDINATE,
                 y=LOCATION_Y_COORDINATE,
                 color=Color)) +
  scale_color_distiller(palette = "RdBu", limits = c(-0.4,0.4))
print(ny.map1)

#temperature
ny.map2 <- ny.map +
  geom_point(data=sites,size=4,
             aes(x=LOCATION_X_COORDINATE,
                 y=LOCATION_Y_COORDINATE,
                 color=Temp)) +
  scale_color_distiller(palette = "RdBu", limits = c(-0.2,0.2))
print(ny.map2)

#CHL/TP
ny.map3 <- ny.map +
  geom_point(data=sites, size=4,
             aes(x=LOCATION_X_COORDINATE,
                 y=LOCATION_Y_COORDINATE,
                 color=CHLTP)) +
  scale_color_distiller(palette = "RdBu", limits = c(-0.000125,0.000125))
print(ny.map3)

Relationship of Chlorophyll and Phosphorous in NY lakes

Sabrina Xie

Last compiled 08 November, 2021, 08:29:22

Linear model of logCHLA~logTP

Initial log-transformed linear model

Scatterplot

Model statistics

Residual plots

Remove outliers and rerun model

Identify outliers

Scatterplot without outliers

Model statistics

Residual plots

Variable effects on model residuals

Relationship of model residuals to lake characteristic variables

Residual plots

Model statistics

Most recent year

Recent year statistics

Color bins

Relationship of model residuals to year by lake

Residual plots

Model statistics

Distribution of slopes